the corona product $gcirc h$ of two graphs $g$ and $h$ isobtained by taking one copy of $g$ and $|v(g)|$ copies of $h$;and by joining each vertex of the $i$-th copy of $h$ to the$i$-th vertex of $g$, where $1 leq i leq |v(g)|$. in thispaper, exact formulas for the eccentric distance sum and the edgerevised szeged indices of the corona product of graphs arepresented. we also study the conditions...

let z2 = {0, 1} and g = (v ,e) be a graph. a labeling f : v → z2 induces an edge labeling f* : e →z2 defined by f*(uv) = f(u).f (v). for i ε z2 let vf (i) = v(i) = card{v ε v : f(v) = i} and ef (i) = e(i) = {e ε e : f*(e) = i}. a labeling f is said to be vertex-friendly if | v(0) − v(1) |≤ 1. the vertex balance index set is defined by {| ef (0) − ef (1) | : f is vertex-friendly}. in this paper ...

All sum graphs are disconnected. In order for a connected graph to bear a sum labeling, the graph is considered in conjunction with a number of isolated vertices, the labels of which complete the sum labeling for the disjoint union. The smallest number of isolated vertices that must be added to a graph H to achieve a sum graph is called the sum number of H; it is denoted by σ(H). A sum labeling...

For a simple path Pr on r vertices, the square of Pr is the graph P 2 r on the same set of vertices of Pr, and where every pair of vertices of distance 2 or less in Pr are connected by an edge. Given a (p, q)-graph G with p vertices and q edges, and an integer k ≥ 0, G is said to be k-edge-graceful if the edges can be labeled by k, k+1, . . . , k+q−1 so that the induced vertex sums (mod p) are ...

Consider the following problem in network design: given an undirected graph with nonnegative delays on the edges, the goal is to find a spanning tree such that the average delay of communicating between any pair using the tree is minimized. The delay between a pair of vertices is the sum of the delays of the edges in the path between them in the tree. Minimizing the average delay is equivalent ...

Let G be a graph of order n. A graph is linear forest if every component is a path. Let S be a set of m edges of G that induces a linear forest. An edge xy ∈ E(G) is called an S-edge if xy ∈ S. An S-edge-length of a cycle in G is defined as the number of S-edges that it contains. We prove that if the degree sum in G of every pair of nonadjacent vertices of G is at least n + m, then G contains h...

the vertex-edge wiener index of a simple connected graph g is defined as the sum of distances between vertices and edges of g. two possible distances d_1(u,e|g) and d_2(u,e|g) between a vertex u and an edge e of g were considered in the literature and according to them, the corresponding vertex-edge wiener indices w_{ve_1}(g) and w_{ve_2}(g) were introduced. in this paper, we present exact form...

Antimagic labeling of a graph with vertices and edges is assigned the labels for its by some integers from set , such that no two received same label, weights are pairwise distinct. Where vertex-weights vertex under this sum all incident to vertex, in paper, we deal problem finding antimagic edge special families graphs called strong face graphs. We prove antimagic, ladder wheel fan prism final...